Northern Arizona Astronomy: measuring distances

Unlike many sciences, in astronomy the researcher can neither run experiments nor manipulate the subjects being studied to determine how things work. Except for the recent probes sent to nearby planets within our own solar system, astronomy is strictly an observational science.

In order to compare the objects we see from Earth, we must first know their distances from us. Since we are unable to use a tape measure to determine these distances, other methods have been developed. Although scientists have been studying stars for thousands of years, it was not until the 1830s, that the use of telescopes that gave astronomers the ability to measure stellar distances using a method called parallax. This procedure is the observed apparent shift in position of an object when viewed from different locations in space. Although by using this approach only the nearest stars can be measured, it provides a standard meter-stick which enables us to compare and utilize other distance measuring methods, and allows astronomers to measure the vastness of space well beyond our general neighborhood, out beyond the Milky Way, and even approaching the farthest reaches of the universe.

To determine distances here on Earth, surveyors use a method known as triangulation, which applies mathematics called trigonometry. Unfortunately, this is not useful when the object is very far away, as are celestial objects. Instead, astronomers use the parallax method, a special type of triangulation, in which the triangles are extremely thin and have very small angles. To illustrate, hold out a pencil in front of you at arm’s-length and view it only with your left eye, then blink to your right eye, and back again. The pencil appears to shift back and forth relative to the distant wall. Next move the pencil closer to your face and repeat the observations, alternately blinking your eyes as before, and again observing the apparent shift of the pencil. Note the shift of the pencil against the wall appears much greater than it did before. As the Earth travels in its orbit around the sun, nearby stars appear to shift back and forth against the far distant stellar background, much like the pencil against the wall. This apparent shift is the phenomenon of parallax. The amount of shift determines the distance from Earth. The further away the star, the smaller is the shift. With orbiting observatories outside our atmosphere, astronomers are limited to observing about 3,300 light years away. Since the Milky Way is about 100,000 light years across, other methods have been developed for measuring greater distances. One of these methods is by utilizing special stars called Cepheid Variable Stars.

Within the 100,000 stars that are measurable using parallax, several thousand of them fall into the category called Cepheid Variables, which have a uniquely characteristic shaped period light curve. In the late 1800s, Henrietta Leavitt at Harvard Observatory, using photographic photometry to determine the absolute brightness of the stars on photographic plates, studied these variable stars and discovered that the periods of Cepheids are related to their actual luminosity. This period-luminosity relationship gave astronomers a new way to measure distances in the universe. By identifying a star as a Cepheid, its variable period could be measured which determined its luminosity. The luminosity distance when compared with the stars visual brightness as it appears in the night sky, can then be determined. Ms. Leavitt observed Cepheid Variables in the two nearby galaxies known as the Magellanic Clouds that orbit the Milky Way in the southern hemisphere, and was able to determine the distances to them, which expanded the size of the then known universe. The large Magellanic Cloud is 160,000 light years from Earth, and the Small Magellanic Cloud is 200,000 light years away. For comparison, the nearest major galaxy to the Milky Way, Andromeda, is 2.5 million light years away, which was also determined using Cepheid Variable stars.

Since then, the distances to much further celestial objects have been determined by additional means, where each of the techniques overlap in range of distance, reinforcing each other and allowing each of the methods to be part of a distance ladder stretching from a few light-years to about one-third the size of the observable universe, which is about 13.8 billion light-years. The techniques used and their ranges are as follows: parallax (4 - 3300 light years); spectroscopic parallax (130 – 33,000 light years); Cepheid Variables (3300 – 100 million light years); RR Lyrae Variables (16,000 – 2.6 million light years); Tully-Fisher Method (2.3 million – 490 million light years); and Type Ia Supernovae (3.3 million – over 4 billion light years.)

Williams Star Party

Members of the Coconino Astronomical Society, in conjunction with the city of Williams, will host a Star Party from 7:30 to 9:30 p.m., at Glassburn Park, in the natural area west of Rod’s Steakhouse parking lot June 2.

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